Journal ArticleDOI
Transverse Vibrations of a Trapezoidal Cantilever Plate of Variable Thickness
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TLDR
In this paper, the natural frequencies of a trapezoidal cantilever plate of variable thickness were determined using energy techniques, and the fundamental natural frequencies for different parameter values were also obtained using a deflection function containing an optimized exponent.Abstract:
N ATURAL frequencies of a trapezoidal cantilever plate of variable thickness, which model an aircraft wing structure approximately, are determined using energy techniques. Characteristic orthogonal polynomials in two variables are constructed to describe the structural deflections, which are used in the Rayleigh-Ritz method to obtain the natural frequencies. The fundamental natural frequencies for different parameter values are also obtained using a deflection function containing an optimized exponent. The first technique can be used to obtain the natural frequencies and corresponding mode shapes for the preliminary design of aircraft wing structures.read more
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Book
Vibration of Plates
TL;DR: Vibration of Plates as discussed by the authors provides a comprehensive, self-contained introduction to vibration theory and analysis of two-dimensional plates, including boundary characteristically orthogonal polynomials (BCOPs).
Journal ArticleDOI
Transverse vibration of simply supported elliptical and circular plates using boundary characteristic orthogonal polynomials in two variables
TL;DR: In this article, the first four frequencies and mode shapes have been computed for elliptical and circular plates of uniform thickness with simply supported edges by employing orthogonal polynomials in the Rayleigh-Ritz method.
Journal ArticleDOI
Numerical experiments on the determination of natural frequencies of transverse vibrations of rectangular plates of non-uniform thickness
TL;DR: In this paper, a comparison of natural frequencies of transverse vibration of thin, rectangular plates of non-uniform thickness with different combinations of boundary conditions is presented, as obtained by using the following methodologies: (1) the Rayleigh-Ritz method with characteristic orthogonal polynomial shape functions; (2) the shape function which includes two exponents that are to be determined by minimizing the fundamental frequency coefficient.
Journal ArticleDOI
On the use of orthogonal polynomials in the rayleigh-ritz method for the study of transverse vibration of elliptic plates
TL;DR: In this article, orthogonal polynomials have been used to study the transverse vibration of elliptic plates with uniform thickness and clamped boundary, and four frequencies and mode shapes have been reported for various values of the aspect ratio.
Journal ArticleDOI
Transverse vibration of completely-free elliptic and circular plates using orthogonal polynomials in the Rayleigh-Ritz method
TL;DR: The Rayleigh-Ritz method using characteristic orthogonal polynomials has been applied to study the problem of transverse vibration of completely-free elliptic and circular plates of uniform thickness.
References
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Journal ArticleDOI
Comments on «natural frequencies of rectangular plates using characteristic orthogonal polynomials in Rayleigh-Ritz method»
TL;DR: In this paper, a set of beam characteristic orthogonal polynomials in the Rayleigh-Ritz method was used to obtain the natural frequencies of rectangular plates. But the results for lower modes were not as good as those obtained by other methods.
Journal ArticleDOI
Natural frequencies of rectangular plates using characteristic orthogonal polynomials in rayleigh-ritz method
TL;DR: In this article, a set of beam characteristic orthogonal polynomials in the Rayleigh-Ritz method was used to obtain the natural frequencies of rectangular plates. But the results for lower modes were not as good as those obtained by other methods.
Journal ArticleDOI
Flexural vibration of polygonal plates using characteristic orthogonal polynomials in two variables
TL;DR: In this paper, a set of characteristic orthogonal polynomials in two variables is used as deflection functions to obtain the natural frequencies and mode shapes of polygonal plates by the Rayleigh-Ritz method.
Journal ArticleDOI
Numerical experiments on the determination of natural frequencies of transverse vibrations of rectangular plates of non-uniform thickness
TL;DR: In this paper, a comparison of natural frequencies of transverse vibration of thin, rectangular plates of non-uniform thickness with different combinations of boundary conditions is presented, as obtained by using the following methodologies: (1) the Rayleigh-Ritz method with characteristic orthogonal polynomial shape functions; (2) the shape function which includes two exponents that are to be determined by minimizing the fundamental frequency coefficient.
Journal ArticleDOI
Technique for Estimating Natural Frequencies
TL;DR: In this paper, the authors generalized the Rayleigh-Ritz direct variational method for the determination of constant coefficients of assumed shape functions by the introduction of arbitrary parameters in the shape functions and illustrated by several simple examples of freely vibrating beams and a plate.
Related Papers (5)
Flexural vibration of polygonal plates using characteristic orthogonal polynomials in two variables
Natural frequencies of rectangular plates using characteristic orthogonal polynomials in rayleigh-ritz method
On the use of orthogonal polynomials in the Rayleigh-Ritz method for the study of the flexural vibration and buckling of isotropic and orthotropic rectangular plates
S.M. Dickinson,A. Di Blasio +1 more